EVERY COPRIME LINEAR GROUP ADMITS A BASE OF SIZE TWO

被引：20

作者：

Halasi, Zoltan ^{[1
,2
]}

Podoski, Karoly ^{[3
,4
]}

机构：

[1] Univ Debrecen, Inst Math, POB 12, H-4010 Debrecen, Hungary

[2] Eotvos Lorand Univ, Dept Algebra & Number Theory, Pazmany Peter Setany 1-C, H-1117 Budapest, Hungary

[3] Coll Finance & Accountancy, Budapest Business Sch, Buzogany St 10-12, H-1149 Budapest, Hungary

[4] Hungarian Acad Sci, Alfrer Renyi Inst Math, Realtanoda U 13-15, H-1053 Budapest, Hungary

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 368卷 / 08期

关键词：

Coprime linear group; base size; regular partition; PERMUTATION-GROUPS; REGULAR ORBITS; SET;

D O I：

10.1090/tran/6544

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a linear group acting faithfully on a finite vector space V and assume that (vertical bar G vertical bar, vertical bar V vertical bar) = 1. In this paper we prove that G admits a base of size two and that this estimate is sharp. This generalizes and strengthens several former results concerning base sizes of coprime linear groups. As a direct consequence, we answer a question of I. M. Isaacs in the affirmative.

引用

页码：5857 / 5887

页数：31

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